What is the extraneous solution to these equations? $\dfrac{x^2 + 22}{x + 3} = \dfrac{5x + 46}{x + 3}$
Multiply both sides by $x + 3$ $ \dfrac{x^2 + 22}{x + 3} (x + 3) = \dfrac{5x + 46}{x + 3} (x + 3)$ $ x^2 + 22 = 5x + 46$ Subtract $5x + 46$ from both sides: $ x^2 + 22 - (5x + 46) = 5x + 46 - (5x + 46)$ $ x^2 + 22 - 5x - 46 = 0$ $ x^2 - 24 - 5x = 0$ Factor the expression: $ (x + 3)(x - 8) = 0$ Therefore $x = -3$ or $x = 8$ At $x = -3$ , the denominator of the original expression is 0. Since the expression is undefined at $x = -3$, it is an extraneous solution.